A full characterization of Bertrand numeration systems

[en] Among all positional numeration systems, the widely studied Bertrand numeration systems are defined by a simple criterion in terms of their numeration languages. In 1989, Bertrand-Mathis characterized them via representations in a real base β. However, the given condition turns out to be not necessary. Hence, the goal of this paper is to provide a correction of Bertrand-Mathis' result. The main difference arises when β is a Parry number, in which case two associated Bertrand numeration systems are derived. Along the way, we define a non-canonical β-shift and study its properties analogously to those of the usual canonical one.

Disciplines :

Mathematics

Author, co-author :

Charlier, Emilie ; Université de Liège - ULiège > Mathematics

Cisternino, Célia ; Université de Liège - ULiège > Mathematics

Stipulanti, Manon ; Université de Liège - ULiège > Mathematics

Language :

English

Title :

A full characterization of Bertrand numeration systems

Publication date :

2022

Event name :

Developments in Language Theory

Event date :

du 9 mai 2022 au 13 mai 2022

Audience :

International

Journal title :

Lecture Notes in Computer Science

ISSN :

0302-9743

eISSN :

1611-3349

Publisher :

Springer, Heidelberg, Germany

Volume :

13257

Pages :

102-114

Peer reviewed :

Peer reviewed

Available on ORBi :

since 21 March 2022

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Bibliography

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